slope ofintercept 13x-11y=-12

{ "query": { "display": "slope intercept $$13x-11y=-12$$", "symbolab_question": "PRE_CALC#slopeintercept 13x-11y=-12" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Line Equations", "subTopic": "Slope Intercept", "default": "y=\\frac{13}{11}x+\\frac{12}{11}" }, "steps": { "type": "interim", "title": "Slope-Intercept form of $$13x-11y=-12:{\\quad}y=\\frac{13}{11}x+\\frac{12}{11}$$", "input": "13x-11y=-12", "steps": [ { "type": "definition", "title": "Slope intercept form defininition", "text": "$$\\mathbf{y=mx+b}\\:$$is the slope intercept form of a line where $$\\mathbf{m}\\:$$is the slope and $$\\mathbf{b}\\:$$is the $$\\mathbf{y}\\:$$intercept" }, { "type": "interim", "title": "Convert to slope intercept form:$${\\quad}y=\\frac{13}{11}x+\\frac{12}{11}$$", "input": "13x-11y=-12", "steps": [ { "type": "interim", "title": "Move $$13x\\:$$to the right side", "input": "13x-11y=-12", "result": "-11y=-12-13x", "steps": [ { "type": "step", "primary": "Subtract $$13x$$ from both sides", "result": "13x-11y-13x=-12-13x" }, { "type": "step", "primary": "Simplify", "result": "-11y=-12-13x" } ], "meta": { "interimType": "Move to the Right Title 1Eq", "gptData": "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" } }, { "type": "interim", "title": "Divide both sides by $$-11$$", "input": "-11y=-12-13x", "result": "y=\\frac{13}{11}x+\\frac{12}{11}", "steps": [ { "type": "step", "primary": "Divide both sides by $$-11$$", "result": "\\frac{-11y}{-11}=-\\frac{12}{-11}-\\frac{13x}{-11}" }, { "type": "step", "primary": "Simplify", "result": "y=\\frac{13}{11}x+\\frac{12}{11}" } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } } ], "meta": { "interimType": "Convert To Intercept Linear Equation 0Eq" } }, { "type": "step", "primary": "For a line in the form of $$\\mathbf{y=mx+b}$$, the slope is $$\\mathbf{m}\\:$$and $$\\mathbf{y}\\:$$intercept is $$\\mathbf{b}$$", "result": "y=\\frac{13}{11}x+\\frac{12}{11}" } ], "meta": { "solvingClass": "PreCalc" } } }